Topological edge states in spin 1 bilinear-biquadratic model

TL;DR

This paper investigates topological edge states in a spin 1 bilinear-biquadratic model, revealing a possible non-trivial gapped spin liquid with chiral edge modes and Majorana fermions, using a fermionic mean-field approach.

Contribution

It introduces a fermion mean-field theory for the model and demonstrates the existence of topological edge states and Majorana modes in a specific parameter region.

Findings

Existence of chiral edge states with gapless dispersion

Majorana fermion states at zero momentum

Power-law decay of edge spin correlations

Abstract

The spin 1 bilinear-biquadratic model on square lattice in the region $0<\phi<\pi/4$ is studied in a fermion representation with a p-wave pairing BCS type mean-field theory. Our results show there may exist a non-trivial gapped spin liquid with time-reversal symmetry spontaneously breaking. This exotic state manifests its topological nature by forming chiral states at the edges. To show it more clear, we set up and solved a ribbon system. We got a gapless dispersion representing the edge modes beneath the bulk modes. The edge modes with nonzero longitudinal momentum ($k_{x}\neq0$) convect in opposite directions at the two edges, which leads to a two-fold degeneracy. While the zero longitudinal momentum ($k_{x}=0$) modes turn out to be Majorana fermion states. The edge spin correlation functions are found to decay in a power law with the distance increasing. We also calculated the contribution of the edge modes to the specific heat and obtained a linear law at low temperatures.